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Unformatted text preview: oldhomewk 13 YOO, HEE Due: Feb 17 2008, 10:00 pm 1 Question 1, chap 6, sect 3. part 1 of 4 10 points A curve in a road is banked. There is a car on the curve. The acceleration of gravity is 9 . 8 m / s 2 . 2 M g = . 1 9 34 What is the component of its weight paral- lel to the incline? Correct answer: 10960 . 2 N (tolerance 1 %). Explanation: Let : M = 2000 kg , v c = 32 . 2149 m / s , Part2 r = 157 m , = 34 , and = 0 . 19 . Consider the free body diagram for the car M g s i n N = M g c o s N | W bardbl- M a bardbl | mg Solution: The car is on an incline that makes an angle with the horizontal direction so the component of its weight parallel to the incline is W bardbl = M g sin = (2000 kg)(9 . 8 m / s 2 ) sin34 = 10960 . 2 N . Question 2, chap 6, sect 3. part 2 of 4 10 points If the radius of curvature is 157 m, what is the ideal speed of the car such that it doesnt rely on friction to keep from sliding sideways? Correct answer: 32 . 2149 m / s (tolerance 1 %). Explanation: Since there is no frictional force keeping the car from sliding sideways, W bardbl = M a bardbl M g sin = M v 2 c r cos v 2 c = g r sin cos v c = radicalbig g r tan = radicalBig (9 . 8 m / s 2 )(157 m) tan(34 ) = 32 . 2149 m / s . Question 3, chap 6, sect 3. part 3 of 4 10 points The next curve that the car approaches also has a radius of curvature 157 m. It is banked at an angle of 30 . The ideal speed for this curve is v c (banked so that the car experiences no frictional force). The speed of the car v s as it rounds this curve is v s = 0 . 649 v c . If the mass of the car is 2000 kg, what is the magnitude of the frictional force needed to keep it from sliding sideways? Correct answer: 5672 . 23 N (tolerance 1 %). Explanation: For this curve there is a new v c since r is different and is different. The frictional force acts either up or down the incline W bardbl + f = M a bardbl = M v 2 r cos = (0 . 649) 2 M v 2 c r cos . oldhomewk 13 YOO, HEE Due: Feb 17 2008, 10:00 pm 2 But we know that at the ideal speed, f critical = 0 and M v 2 c r cos = W bardbl ....
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